arXiv 1002.26512010-02math.AGmath.KT

奇点的Z[1/p]-模奇点的分解

Z[1/p]-motivic resolution of singularities

Mikhail V. Bondarko

备注：: Some minor corrections made; to appear in Compositio Mathematica
发表信息：: Compos. Math. 147 (2011), no. 5, 1434-1446
DOI：: 10.1112/S0010437X11005410

摘要：

本文的主要目标是推导（从最近的奇点的分解结果Gabber）以下事实：（有效）周动机与$Z[1/p]$ -系数在一个完美的领域$k$的特征$p$产生类别$DM^{eff}_{gm}[1/p]$（有效的几何Voevodsky的动机与$Z[1/p]$ -系数）。因此，$DM^{eff}_{gm}[1/p]$可以被赋予以$Chow^{eff}[1/p]$为核心的Chow权结构$w_{Chow}$（权结构在前面的论文中介绍，其中还证明了$DM^{eff}_{gm}Q$的$w_{Chow}$的存在）。如前几篇论文所示，该陈述立即得出保守权重复函子$DM^{eff}_{gm}[1/p]\to K^b(Chow^{eff}[1/p])$的存在性（它导出$K_0$ -群上的同构），以及典范和函子（Chow）-权重谱序列的存在性和任何上同调理论的权重过滤$DM^{eff}_{gm}[1/p]$。我们还定义了$DM_{-}^{eff}[1/p]$的一个Chow t-结构，并将它与非分歧上同调联系起来.为此，我们研究双有理动机和双有理同伦不变层与转让。

英文摘要：

The main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with $Z[1/p]$-coefficients over a perfect field $k$ of characteristic $p$ generate the category $DM^{eff}_{gm}[1/p]$ (of effective geometric Voevodsky's motives with $Z[1/p]$-coefficients). It follows that $DM^{eff}_{gm}[1/p]$ could be endowed with a Chow weight structure $w_{Chow}$ whose heart is $Chow^{eff}[1/p]$ (weight structures were introduced in a preceding paper, where the existence of $w_{Chow}$ for $DM^{eff}_{gm}Q$ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor $DM^{eff}_{gm}[1/p]\to K^b(Chow^{eff}[1/p])$ (which induces an isomorphism on $K_0$-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on $DM^{eff}_{gm}[1/p]$. We also define a certain Chow t-structure for $DM_{-}^{eff}[1/p]$ and relate it with unramified cohomology. To this end we study birational motives and birational homotopy invariant sheaves with transfers.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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